


cartesian coordinates

by wildcard_47



Category: Mad Men
Genre: Alternate Universe - High School, F/M, Tumblr Prompt
Language: English
Status: Completed
Published: 2014-09-09
Updated: 2014-09-09
Packaged: 2018-02-16 17:06:38
Rating: Not Rated
Warnings: Creator Chose Not To Use Archive Warnings
Chapters: 1
Words: 9,350
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/2277813
Author URL: https://archiveofourown.org/users/wildcard_47/pseuds/wildcard_47
Summary: <blockquote class="userstuff">
              <p>It was typed at the top of her class schedule in bold black letters. <i>Calculus. 8:30am.</i></p>
            </blockquote>





	cartesian coordinates

“I'm sorry. There must be some mistake.”

It was typed at the top of her class schedule in bold black letters. _Calculus. 8:30am._

Joan tucked a strand of her red hair behind her ear, shifting in the hard wooden framed chair and fixing dumpy Mr. Rutledge with the most gracious smile she could muster. The guidance office was dingy and cramped; she only came in here once a year to have her final schedule approved, and now—

The guidance counselor smiled back, seeming amused by the mix-up. Jesus. Was he _enjoying_ this? “You took algebra three last semester, Joan, and passed with flying colors. Mr. Cooper was very complimentary of your work. I don't say that lightly.”

Joan's sure. He spent half the lessons singling her out for extra questions. She hadn't even wanted to earn another math credit, but algebra was a breeze, and full of boys, and Kate had begged her to switch in. She needed help with the homework.

“Mr. Rutledge, I just don't think it's _necessary_ for me to take calculus,” she pressed, letting her hand flutter to her heart, a sudden idea dawning. “When would I ever need to use it?”

**

“How was I supposed to know he studied math in college? It takes him half a year to perfect the social budget for student council! I could set that in two months, for god's sake!”

Leaning against the yellow-tiled ledge beside the narrow bathroom windows, Kate just watched as Joan paced in front of the sinks, and blew out a breath of smoke, passing the cigarette they were sharing back to Joan, holding it between her finger and thumb.

“Well, it could be worse. Ken Cosgrove is in that class, you know.”

There was a smokers' courtyard, of course, but it was always so crowded in the mornings. And full of pleasant distractions. Joan just wanted ten minutes alone with her best friend to be angry.

“He is cute,” she agreed, taking a drag of the cigarette, and thinking about Kenny's bright blonde hair and easy smile. “Not as handsome as Roger, though.”

“True,” Kate accepted the cigarette back, and stubbed it out on the side of the sink bowl, near where one of the screws held it to the wall, then tossed it into the trash. “Although I never necked with Roger at freshman homecoming. You could be biased.”

Joan pursed her lips in a small smile, swatting at her friend's arm with one hand. Fortunately or unfortunately, Roger had graduated three years ago. She still missed him. “Shut up.” She checked her watch, pulling an unhappy face. “Ugh. I should go.”

“Mr. Cooper would never give you detention,” Kate says with a wink, as Joan gathers her books and takes one last look at her reflection in the mirror. Her scoop necked purple dress is brand new, and this updo suits her. She should start wearing her hair like this more often.

**

When she got to class, there was only one chair left, in the second row, beside a freckled boy in a jacket and striped tie, with thick-framed black glasses, a thatch of sandy red hair, and a stack of textbooks and loose-leaf papers placed in front of him.

_Jesus, what a geek. He must live for this kind of thing._

She took her seat quickly but didn't bother to open her book. The first day of class was always spent going over the syllabus in consummate detail, having a small discussion about Mr. Cooper's goals for the year, and being assigned study partners. Joan wasn't worried. He wouldn't care if she never cracked the book in class, so long as she wasn't talking, could answer a question when called on, and performed well on the tests. Algebra three had been the same, although after the first couple of weeks he had taken her aside to warn her about playing stupid. At the time, she'd been trying to impress one of the baseball players, and it had worked—she thought about the way Lee's hands had ghosted up under her bright cheerleading sweater—but not because of anything she'd done, or hadn't done, in math class.

Mr. Cooper was now reading off his list of assigned study partners. Joan let her focus drift in and out; she knew most of her classmates from various sports and social events. Athletes, student council, college preparatory track. “Abbott—Zeller. Adams—Smith. Brent—Romano.”

She picked up her pen and busied herself writing a calligraphic J in the corner of her notebook when she heard her name called.

“Holloway—Pryce.”

She looked up, not recognizing the name, then to her right, where the spectacled boy was staring at her in clear horror.

“You'll sit next to your study partners for the rest of term,” Mr. Cooper continued in a clear voice, unamused eyes sweeping the class for possible contention. “Assume your new seats, please.”

Amid the shuffle of papers and books and people settling back into their chairs, she and her new study partner stared at each other for at least ten seconds, as if daring the other to get up and choose a new pair of seats. Neither of them moved. Joan decided to at least try at being friendly.

“I'm Joan,” she said, with a confident smile. “If we're going to work together, we may as well be introduced.”

He blinked back at her, owlish, and seemed annoyed. “Lane Pryce.”

His accent surprised her. “You're English?”

“Yes,” he huffed, like it was frustrating to explain even this much to her.

A throat clearing from the front of the room made her startle, and turn quickly back to the front of the room, as Mr. Cooper resumed his lesson.

**

“Joan, I still can't believe you're taking calculus!” Trudy poked with a fork at the bowl of steaming french fries she had bought for lunch. She was only going to eat one or two, of course. “Couldn't you tell Mr. Rutledge you don't need it?”

“She tried,” Claudia said with a sigh. “Did you not hear us talking in study hall?”

Joan arches an eyebrow, raising her voice a little. “She was watching Pete Campbell in his tennis whites.”

The table broke out into giggles. Trudy blushed, and put down her fork with a clatter. Two tables over, Pete—who wasn't even a senior, but was sitting with his older brother—didn't seem to have heard a thing.

“Hey, Joan,” comes a voice across the senior section, and it's Greg Harris, all broad shoulders and boyish smiles. Joan pretends not to hear that he's teasing her, but blushes prettily under his attention. “Saved you a seat, if you wanna come over.”

“Will you be at practice?” Joan asks loudly, looking back at him with a coy smile and a little tilt of her head. “We've got some new cheers.”

“Heard from Coach Rumsen you girls got new uniforms this year, too.”

**

The first week of school flew by. Joan began to look forward to her morning routine: chatting in the right front corner of the bleachers with Kate, and Greg, and Claudia and her boyfriend Bill and his sister Elizabeth, and anyone else from the team who happened to pass by that part of the gym. Greg usually threw paper balls at the freshmen as kids scurried past on their way to their lockers—the dungeon—or tried to shoot hoops with some of his friends. They weren't very good. Although he wasn't good at football, either, and nobody seemed to care about that.

Eight thirty meant calculus and stupid Lane Pryce, who seemed intent on staying quiet while hating everything she did. He kept glaring at her. Joan took breezy notes in shorthand on two days—so far the lessons were little more than basic functions, which they'd covered at the end of last semester in algebra three—but spent most of the week just trying to irritate him without saying a word. It was so easy to get under his skin. If Joan were being honest, she kind of enjoyed that.

Today, she'd broken a nail while opening her locker, the jagged edge now digging into the side of her finger whenever she picked up her ballpoint pen. So, she took out a nail file from her purse, relishing the look of outrage on Lane's face once he saw it, and spent several minutes patiently buffing the sharp corner back into its usual oval shape as she listened to the lesson. Mr. Cooper continued talking about velocity and the rates of change, how they pertained to this course, but suddenly—

“Miss Holloway? I believe you can tell us why the average rate of change is important, in this particular case.”

Lane actually laughed when Mr. Cooper called her name. She heard it. The sound was quiet—the smallest huff of breath, barely noticeable to anyone else, but it made her furious—and so she turned a sunny smile on their teacher in response, folding her hands on top of her notepad. She even decided to give the full answer just to prove to Lane that she didn't appreciate his making fun of her. “Well, when expressed as a function, the average rate of change is known as a derivative.”

The teacher held out his piece of chalk in her direction. “If you will write the full equation on the board.”

“Of course.” She uncrossed her legs and stood up in one fluid motion, taking the chalk from Mr. Cooper's hand and moving to the middle of the blackboard. One of the boys in the back whistled like he was cat-calling, and Joan let herself laugh in response, although the teacher reprimanded the culprit. Was that Paul Kinsey? It seemed like something he'd do.

The chalk clicked against the black slate as she wrote: _f(b)-f(a) ÷ b-a ._

“Can you explain each variable?”

“It's the end point, f-b, minus the start point, f-a, divided by region,” Joan clarified.

“And it can also be known as?”

“The change in location, divided by the change in time.”

“Very good, Miss Holloway. You may take your seat.”

As Joan sauntered back to her desk, she noticed Lane staring at her, eyes wide behind his glasses, and mouth open a little, like she'd completely stunned him. She made a little satisfied noise as she sat down, and replaced her nail file in her purse, purposefully not looking in his direction.

Cooper had already moved on to the next question. “Mr. Pryce, can you explain the more formal equation for the change of location divided by the change in time? If the time change is not gradual, but instantaneous?”

Lane bolted upright, swallowing once before he spoke. “Erm. Yes. It's—well, the region of time we care about, at that point, would be—zero, obviously, and so—”

It took him almost a minute to sputter out a full response, although in the end his answer was so detailed it caused someone else to whisper a joke, because there was an obvious snicker from the group in the back left corner. Joan caught the word _geek,_ and rolled her eyes _. Boys._

Lane didn't seem to notice, and wrote down the newest equation from the board into his notes with stiff precision. She dutifully copied down the same in her own notebook.

**

After the second home game of the season—they beat A.C. Clemmons!—there was a party at the shake shop, Mel's, just down the road from the high school. Half the senior class was there. Joan spent most of the party with a few girls from the squad and their boyfriends in a back booth, until Greg's wandering hands indicated he wanted to go someplace more private. He had his own car, which his father had bought, and they drove up to Howard's Knob: a bluff overlooking the biggest intersection in town from a distance, nestled just inside a small grove of trees. Kids parked here all the time.

In the backseat, Joan shuddered as Greg slid a hand further up her skirt, pitching forward against him with a whine as his fingers trailed against the front seam of her panties. He didn't touch her the way she wanted, though; his hand moved inside her, pushing and prodding against her taut muscles like she was having a yearly physical. It didn't hurt—it just wasn't good, and she bucked her hips up, needing something better. He moved his hand slightly, accidentally hitting the right spot—once, twice—more often than not, now, and Joan gripped the shoulders of his collared shirt in two fists, her breath coming faster. “Oh—god, press there, you can feel it, please—”

Greg stopped what he was doing, staring down at her, his free hand now gripping her shoulder instead of her hip. “What the hell is that supposed to mean?”

She gaped at him, mind still blurry with need, not understanding. “I—just—”

He withdrew his other hand, wiping it on the leg of his pants, and roughly moved her from his lap. “Are you not having a good time?”

“What?” she sputtered, watching him fold his arms across his chest, and quickly reaching out to touch his shoulder. “No—Greg, I just—like talking, is all. When you're doing that. I—”

“You know, my girls have never had a problem with the way I take care of 'em,” he hissed, pushing her hand away. “Ever!”

“I didn't mean to put you down,” she insisted in a quiet voice, feeling anger quietly replace what interest she'd had from his earlier petting. For god's sake, it wasn't even about having a good time at this point—he'd been so eager for her in the beginning that he'd pushed her head down toward his zipper almost as soon as they'd climbed into the backseat. “Greg, please—I wasn't trying to insult you.” She takes a breath, trying not to lose her temper. “I liked it, okay?”

Jesus, what else was she supposed to say? Most guys loved it when girls lost their heads: as a freshman, when she was going steady with Roger Sterling, he couldn't get enough of it.

(But he'd been _good_. And he'd liked hearing what she wanted.)

Greg refused to look at her, his boyish jaw set in a pout. “I don't give a shit! You don't ever tell a guy off when he's doing things for you!”

She'd fixed her eyes on the rear door handle of the car to the left of the driver's side window, which rocked and creaked on its tires like the people inside were having the time of their lives.

“Greg—”

“Stop talking to me. I'm taking you home.”

**

On Monday, the girls claimed they were reducing for homecoming, so they were just going to smoke a cigarette or two instead of eating lunch. Joan was welcome to join them, they said. She had gamely thrown away her fruit cocktail and gone outside with them. But once they were standing in the shade in the courtyard, no one pressed her to make conversation. The girls didn't talk to her very much at all, and so she'd left early, claiming a stomachache.

Tuesday, Claudia and Bill and Greg and Elizabeth and all her usual friends weren't in the gym before classes. She couldn't find them anywhere, and all day, in the corridors—in classes—even at practice, Joan started to hear whispers at her back. _Hey, Hallway. Press here for a good time. Hiya, fastball. Want to go parking?_

Wednesday, she'd seen Greg in the lunchroom after buying a cherry soda. He'd given her a look that could have frozen ice, and said something to his friends that made them howl with laughter, not even bothering to whisper. She only caught three words—

_begged for it_

_—_ and lost her temper completely.

Two minutes later, the palm of her hand stung as she practically ran away from his table. Greg had a red hand print on his cheek, and cherry soda staining his shirt, and was screaming insults in her direction. The rest of the cafeteria was hooting and jeering, and two other seniors were holding Greg's arms behind his back to keep him from running after her.

Mr. Rutledge was the lunch monitor, and saw it all happen, but he didn't give her detention. The pitying expression on his face as she sat in his office listening to him lecture her about going steady and how decent girls behaved with their beaus was a thousand times more embarrassing than any punishment he could have issued.

Thursday night, Joan talked to Kate on the phone; her friend had bronchitis, and sounded awful. _Jesus._ Between coughs.  _Did Ida kick you off the squad?_

_It'd be best to take a few weeks off. That's what she said._

_She's not an official coach, you know. She's just some unpaid volunteer._ More coughing. _You don't actually have to listen to her._

 _I still hate seeing him on the field,_ Joan had whispered in a savage voice, staring at her letter sweater from where it hung on the doorknob across the room. The sound of keys jingling came from the front door. _Shit._ _Mom's home— I have to go._

Friday morning, Joan walked into Mr. Cooper's classroom and sat down at her usual desk ten minutes before class began. She folded her shaking hands into her lap and pretended she was just studying, although her book was open to a unit they wouldn't even start until spring.

Class began with a pop quiz on inverse trigonometry functions. She read over the first question six times before realizing she still couldn't remember what it was asking her to solve for, and just turned her blank paper over without filling in an answer, fixing her eyes on the blackboard and listening to the frantic scribbles of pencil against paper.

She only spoke once, when Mr. Cooper called on her to solve for _sin_ (∂) in an equation he'd written out from the quiz.

“I—” she sputtered, flushing red with embarrassment, which made a snicker pass through the room. She heard another snide remark from the back, over everyone's laughter— _press here, Hallway—_ and pursed her mouth to keep herself controlled, staring down at the arm of her desk until a scrap piece of paper was suddenly tucked under her right forearm, the note passed unseen amid Mr. Cooper's reprimand to the cut-ups in the back left corner—

 _3_ _π_ _÷ 2_

“Three pi over two,” she quickly said once order was restored, and wasn't called on again.

When class was finished, she gathered her books and walked purposefully toward the back of the building—through the three hundreds and down the back stairs, making a sharp right and moving along the corridor until the four hundreds turned into the junior lockers, and then the hallway by the weight rooms. At the end of this hall, the double doors which led outside to the track and bleachers were finally visible. She hurried through them, bright sunlight now stinging her brimming eyes, and moved toward the bleachers at a run before reaching them. She flung her books onto the ground, sat down in a slumped position against the wall of the concrete stairs, and put her head in her hands.

After a minute of hysterical crying, someone cleared their throat behind her, and she looked up in a panic to see Lane Pryce standing at the top of the stairs, her calculus notebook in his outstretched hand.

“You dropped it,” he blurted out, watching her nervously, as if he was surprised, as if he didn't know what else to say. “Sorry—I don't mean to—pry.”

She started blubbering again, shielding her eyes with one hand and turning away. After a pause, he came closer, took a seat next to her, and put a palm on her shoulder. It just made her cry harder.

_God, he hates her and he's still offering sympathy; she must look horrible._

“My boyfriend dumped me,” she sobbed in a rush, feeling stupid just by saying it, “and he's spreading all these awful rumors—and I got kicked off the squad—and my best friend's out sick and no one else will talk to me—”

She snorted and swallowed the rising congestion in her throat, cringing at how disgusting she sounded, but Lane didn't seem upset by this. When she snuck a look to her right, he was just sitting there, solemn and still. He rubbed his free hand across the back of his neck, staring out onto the empty football field. In the distance, one of the coaches was cutting the grass with a push mower, threading between the goalposts as he worked.

Joan suddenly wondered if Lane had many friends at this school, or any at all. She never saw him in the lunch room, or in the hallways most mornings. He didn't seem like the type to come to any of the games, or hang out with many of the popular kids, and suddenly she felt guilty that he came all the way out here, for her. Maybe he was in one of the academic clubs.

“I'm sorry,” she said, wincing at the way her voice cracked over the words. “You must think I'm just some...stupid cheerleader, upset over nothing.”

 _Hallway. Hallway._ She set her jaw to keep a fresh wave of tears at bay.

“You're _not_ ,” he blurted, “that is—it isn't—oh, hell.” He let out a sigh, like he hated getting so tongue-tied, and after a moment, spoke again. “Your boyfriend's an idiot,” he said finally—voice quiet, like he was waiting for her to be offended on Greg's behalf. “And you're not stupid.”

His hand was still on her shoulder, his thumb brushing across the top of her upper arm. It was sweet of him to try and cheer her up. For the first time in almost a week, Joan felt a little better.

“You think so?”

Lane smiled at her. He had a nice smile. It made him look kind. “As your—official calculus partner? I know so.”

She was so surprised at his trying to make a joke—dumb as it was—that she actually laughed.

“I don't think I've ever missed class before,” he said after another pause, suddenly looking alarmed, like it was just occurring to him that second period would continue in his absence, and she laughed even harder, swiping away a few stray tears from her cheeks.

**

She started spending mornings in the library with him, before class.

Sometimes they studied—Lane brought out the most embarrassing set of handwritten flash cards to drill her on limits and discontinuous functions, which she had trouble keeping straight. Thankfully, she got him back when they moved on to complex conjugates—he hated imaginary numbers with a passion, and when he made an 86 on the unit test, which was his lowest grade to date, Joan heard about nothing else for two straight days.

“No, that's because there is no _practical_ _use_ for complex conjugates—why on earth would anyone bother positing for the value of A, minus the imaginary number, when they can simply project, through a— _simple_ algebraic equation using real values and _legitimate_ mathematics—”

“Lane,” she groaned, reaching to pull his dog-eared test paper away from him, and smirking when she ended up having to wrestle it out of his hands. “For god's sake. It's on the final exam, so you have to learn it. We'll just—study harder.”

He had frowned then, because to his logical brain there was no good comeback for something as immutable as _it's on the test_ , and sighed like she had just told him the end of the world had arrived. “Well, I shan't. I think it's ridiculous.”

She loved seeing him get all prim and huffy. It always made her smile. “It'll be fine.”

Sometimes they just talked, about school and their classmates and radio programs and college applications. She learned that he had only come to America because of the war. Before the bombings in London, his mother had sent him to live with her sister. He liked it here, but missed her very much.

Kate even stopped by to chat occasionally—being a student council officer kept her very busy, but they met in the library if Mrs. Katz's classroom was occupied—and gradually, so did a couple of the younger girls from the squad. Not Claudia and Elizabeth, though. Joan never thought she'd be happy to step away from cheerleading, but when Hildy Masterson turned up pregnant (she heard) and Ida offered Joan her old spot back on the team, she decided not to do it. She'd felt relieved at not having to plaster a smile on her face for the majority of the day. Especially when it meant not seeing Greg. He was on the basketball team, too—even if he just rode the bench all season.

Lane didn't say so, but she knew he was proud.

The day before they left for Christmas break, Joan walked up to their usual table with a single sheet of sketch paper in hand, tied into a roll and held closed by a red ribbon. When she handed it to him, as solemnly as if presenting him his diploma, Lane stared at her in shock.

“What's this?”

She shrugged, still unsure why she wanted to give him a Christmas present at all. It was her first thought as soon as the new art teacher let her take it out of the display case. _Lane would like this._ “Oh, I did it for class. It's not much, but I thought you might...appreciate it.”

He unrolled the sketch paper to reveal a small pencil drawing of Big Ben. Their assignment had been to pick a piece of foreign architecture. Joan thought the face of the clock had turned out nice, but there were smudges on both sides where she'd had trouble establishing three-dimensional perspective, and the intricate scrolls at the top had turned out crooked, which she hated. It wasn't a very good rendering, but she couldn't quite bring herself to throw it out, either.

“You're really quiet,” she said, sitting across from Lane and wrinkling her nose as she watched him stare at her silly little drawing. “Is it that bad?”

“No,” he said in return, smoothing the corners of the paper down with his fingertips like they were as fragile as glass. “Joan, it's—so pretty.”

“Oh. Well—I'm glad you like it.”

She had pretended not to care about his reaction either way, but she felt the compliment ring around her head for the rest of the day, and a pleased warm feeling hovered low in her stomach, even after she got back a failed biology quiz in fourth period.

On her birthday, Lane spent their first twenty minutes in the library not quite meeting her eyes across the table, and when it was nearly time to go to class, he plucked a folded piece of paper from his notebook, scooting it toward her with a careful hand. “This...is for you.”

Joan stared speechless at the front page for at least ten seconds—HAPPY BIRTHDAY was written in big, colorful print—surprised and thrilled that he had remembered. She opened it to see what he had written inside.

On the left page was a list of notable historical events that had also happened on February 24th. It looked like a book report. _Date of leap year for the typical Julian calendar. Premiere of Handel's first Italian opera on the London stage, 1711._ She had no idea how Lane found all of this out; he must have spent half of his free time in the library working on this. Was that why he'd refused to come out to any of the Friday student council dances? She'd been nagging him to bring a friend for weeks.

On the right hand side was a short notation, written in his usual painstaking cursive. _Joan: an English derivation of the Old French name Johanne, which is in turn the female variant for its male counterpart Johannes. Often interpreted as one who has been favored, or, God is gracious._

“I can't believe you did this,” she murmured, and jumped up to hug him. He was so surprised he dropped half his books into the floor, but when she let him go he was grinning.

“Oh—well, it isn't much—had a friend look up the French translations.”

In the spring came baseball season, and a huge surprise.

“We play Freedom today,” she reminded Lane, after the fourth guy in full baseball gear had walked by their study table.

“Yes, I know that,” he retorted over the top of his English textbook, like this was obvious. “Although we'll be lucky to scrape through, given last week's incredible fiasco. I don't know what Wallace was doing, but he certainly wasn't playing very well.”

In the eighth inning, Cody Wallace fumbled a catch as the ball sailed past third base and into the outfield, and as he was sprinting to retrieve it, Matthews cleared the bases and won the game by four extra runs.

“Wait—did you— _go?_ ” Joan asked, staring at him like he'd just sprouted a second head.

“You don't know everything about me,” he grumbled, as if her surprise was annoying—but when Joan laughed in delight, his humor shone through. A little secretive smile played around the corners of his mouth. After that, he'd shown her the pocket-sized notebook he carried in his front jacket pocket—filled with an incredible list of baseball statistics: national teams, school conference scores. His handwriting filled pages and pages, and for a second, she was so fond of him she wanted to burst.

“This is amazing,” she said after a minute, and meant it. “I want to go with you. Show me all of this as it happens.”

 _If it's not weird,_ she meant to add, but didn't.

He blushed to the roots of his hair. “Er—well—will you, then?”

**

“Oh, hey, Lane,” said a plain-looking girl near the dugout, as they picked their way into the top of the stands.

He waved to her. She was the third or fourth person to say hello since they'd gotten to the field. Joan was glad to see so many people knew him here. “Jerry doing—all right, then?”

The girl shrugged. “His shoulder's hurting him. Coach Peterson says he's okay to pitch.”

“Both juniors. Jerry's her boyfriend,” he explained to Joan, as they took their seats. “Little sister's here somewhere, as well.”

There was a little pale-eyed girl standing at the top of the stands, no more than ten, her hands braced on her skinny hips as a barrel-chested sophomore went up to bat first. Joan recognized him from football, too; he was first string, this year. Strong kid.

“Staaaaan,” the girl yelled, cupping her hands around her mouth in order to be heard over the crowd. It was working better than should have been possible, given how tiny and mousy she looked in her black Mary Janes, green plaid skirt and white blouse. Joan glanced back, covering her mouth to hide a laugh, watching this little Catholic kid try to taunt a high-school boy. “You hit like a baby!”

Lane was grinning, and when he leaned over to whisper in her ear, Joan found out why. “Happens nearly every week. Or—whenever she's here, I suppose.”

“Staaaaan! Don't strike out! Don't strike out, Stan!”

Joan couldn't help turning around, raising an eyebrow. “Don't you know you're supposed to jeer the other team?”

The little girl blinked down at Joan like that was the strangest response in the world, blowing her wispy bangs out of her face. Her voice was prim and high-pitched. “He called me a shrimp.”

“Well,” Joan managed, and had to turn back around so the little girl didn't see her giggling. Lane noticed it, though, and elbowed her in the ribs in between writing down a couple of statistics.

The sun sunk lower in the sky, and the stands filled with people, and Joan couldn't remember the last time she had so much fun. Lane showed her what he was writing down, and why—how each player's RBI could be calculated based on a certain number of variables, what it meant mathematically when someone only got to second base instead of rounding home plate, or how to factor in aspects like when the first baseman missed an important catch.

It felt a little like talking about calculus, only much more social. She loved it.

They shared some Cracker Jack that Joan bought with her pocket money, and—a little later—Lane got up during the seventh inning stretch and came back with a couple of plain hot dogs and two cokes in glass bottles. The frankfurters were burnt to a crisp, and the buns were hard as rocks, but when Dick Whitman hit a key home run in the top of the eighth inning—and Lane accidentally pelted his hot dog into the back of someone's head, he cheered so wildly—Joan laughed until she felt faint, and on an impulse, threw her arms around his neck.

“Thanks for bringing me. This is really fun.”

He stiffened in her embrace—and then—she felt his palms come to rest gently on the side of her hips, just where the hem of her skirt met her blouse, and she _knew_ what that meant _—_ and he hadn't intended to do it; it was obvious from the way he yanked his hands away and stepped backwards—shock and embarrassment written all over his reddening face.

Oh, my god.

Joan felt flushed. She could barely look at him. He was fumbling with his notebook again.

“Hey!” snapped the little girl from behind them, stomping one foot on her bleacher seat as if to get their attention, “Harry Crane just tripped over his shoelace, and _you_ _missed it!_ ”

**

After the game, Lane excused himself to get another soda, or something. Joan barely heard the excuse he gave her—she wasn't really paying attention—but after he'd been gone for almost half an hour, she began to get worried. She picked her way through the celebrating team, and the excited parents, and the last of the dejected kids going back to their district on a ten o'clock bus.

“Hey, Joan,” said someone behind her—she whirled around to see Ken Cosgrove, who motioned her over. “Listen, if you're looking for Lane, I saw him earlier—and it's not good.”

Joan hurried around the back of the building before she finally found him. He was sitting slumped against a wall, cradling the side of his face in one hand. When she walked closer, in the dim glow of the nearest streetlamp, she could see some of the damage. There was a tiny smear of dried blood under his nose. One of his eyes was bruised and swelling.

“What happened?” she asked, covering her mouth with her palm. He glanced up to look at her, one shoulder lifting in a shrug. She went to sit beside him. “Do you at least know who it was?”

“Yeah,” he said, voice rough, like he wanted to cry. “It—doesn't matter.”

“Lane, it matters to _me,_ ” she replied fiercely, reaching out to grip his hand. His knuckles were rough and scabbed against her palm—he fought back, she realized with a jolt. “They hurt you, for god's sake.”

“Not the first time he and I've had words,” he mumbled, like he was embarrassed to say this out loud. “He hates me. You don't have to act surprised.”

The only person she knows Lane hates—besides Greg, who probably wouldn't know Lane if he had to pick him out of a lineup—is Pete Campbell. And they had a home tennis match today; he might have still been hanging around the school, with his brother, or some of his snobby friends.

“No—he doesn't get to _do that,_ ” Joan insisted, her voice very low. Her fingers threaded through the hair near his temple, still damp with sweat. “You're sweet, and you're smart, and he's just jealous because you—”

She didn't even get to finish the sentence because his mouth was suddenly on hers—hungry and hot. But almost as soon as the kiss had begun, Lane was pulling away, looking ashen, leaving Joan stunned.

“God,” he whispered, looking crushed, “I'm—I don't know why I did that. I'm sorry.”

For the first time in her life, Joan didn't know what to say, and before she could recover, he had pushed himself into a standing position, walking away from her and towards the parking lot. She knew he wanted time alone. She wanted to follow. She couldn't make herself go after him.

He wasn't in school the next day, the first time he'd been absent all year.

**

“Joanie, are you gonna eat that, or am I going to have to save it for your dinner?”

Joan sighed, and pushed her plate away. Mom hated it when she'd waste food; not that either of them ate very much for breakfast. In this town, on a waitress's tips, it was hard to do more than keep the lights on and a roof over their heads. But they usually had something light around the house: eggs, some sandwich ingredients, and the chocolate diet drinks her mother was obsessed with.

“I think I might go to the library today,” she said instead, putting her untouched egg into an uncovered bowl, and placing this back into the fridge.

“On a Saturday.” Gail stared at her daughter like she'd just grown a pair of horns, or offered to drive them both to church.

Joan set her jaw, and said nothing. Her mother rolled her eyes, gesturing to her apron strings.

“Well, then, help me tie this in the back before you go to _the library_.”

Emphasizing the last two words, like she was fully aware Joan was lying.

Well, she _was_ lying. So what? Why did her mother have to be so annoying all the time?

**

She'd looked up the address for Lane's aunt in the phone book. Waverly Avenue. It was on the same side of town as the high school.

Kate drove her there—Kate, who grinned like a little demon when Joan finally told her she and Lane had gone to the baseball game together—and who'd also made appropriate noises of sympathy when Joan admitted what happened afterwards.

Kate started making conversation after a few minutes of driving, in an attempt to distract Joan from her own nervousness. Her friend's blonde hair was curled loosely today, and was flowing in the breeze which drifted in from the driver's side window. “You know, you should be on the lookout for your college letters. I got one back already.”

“Jesus,” Joan exclaimed, feeling horrible because she hadn't asked. “Radcliffe?”

Kate rolled her eyes, and that was answer enough. “I'm not really upset. Dad was the one who wanted me to go. He just liked the idea. You know I never cared about that.”

“If I go anywhere, I'll be doing better than my parents,” Joan said quietly.

“You'll get into NYU,” Kate replied, glancing at Joan with clear, confident eyes. “I know it.”

Joan shifted in her seat, feeling her heart start to pound a little faster as they took a right onto Waverly.

“That is, if you don't end up marrying Lane and having his skinny English babies.”

Joan shot her friend a look that said she would have killed her, if Kate wasn't also doing her the biggest favor in the world. “Excuse me for not mooning over Frank the hunk and his _amazing hands_.”

Kate started laughing, and Joan smiled, too. She started to feel a little better until her friend guided the car to the left-hand curb, just in front of a little blue house with yellow shutters.

“You said one thirty one, right?”

“Oh, god,” Joan said dully, staring at the closed blinds with panic rising in her stomach. “Katie—girls aren't supposed to do this.”

“You're not _girls_ ,” her friend said, patting Joan's knee in a cheerful way. “You're Joan. Now get out of my car before I ding-dong-dash.”

**

The only thought left in Joan's head, after the doorbell rang and she was left to stand on the steps with her hands shaking and her legs like rubber, was that she hoped his aunt wasn't home. Oh, god, please don't let her be home. Please let him come to the door. What if he's not even—

The door opened, and Lane stood there in a white t-shirt and his school trousers, suspenders standing out bright blue against the cotton of his shirt. Jesus. Without all his school layers, he was much more broad-built than she had guessed.

His mouth was hanging open, face flushed pink from his neck to the tips of his ears. “God—I—thought you were my aunt.”

“Can I come in?” Joan asked.

After what felt like an eternity, he nodded yes, and ushered her inside. They went into the living room, which was close to what Joan had pictured in her mind. Lots of lace and delicate china teacups and pink-cheeked ceramic figures.

“Do you—can I get you—anything?”

She shook her head, taking a seat on the nearest end of the powder-blue sofa. “You weren't in school Thursday and Friday.”

“Oh,” he said quickly, voice dull. “Erm. Suppose I missed something, then?”

“No. I was—worried,” Joan finished, and felt herself flush. “I almost called you, but I didn't want your aunt...” she sighed, lifting one hand in the air. “I didn't want her to snoop.”

“But you're here,” Lane said after a slight pause, like this was the part which was confusing him. “And she's—not.”

“I know,” Joan said, staring fixedly at a collectible plate with the face of a white kitten on it—and suddenly she felt like she just had to show him. It would be easier to do this if she didn't have to stumble through the words. When she felt confident enough to meet his eyes again, she saw he was staring at her in a way that made hope bloom hot in her chest.

She got up, strode over to him, and kissed him like he was a soldier leaving for the Pacific front.

“Oh, my god,” he said when she pulled back, sucking in breath after breath like this was the best thing that had ever happened to him in his entire life. “You—”

“Shut up,” Joan interrupted with a grin, and kissed him again. He made a muffled noise, his hands moving to rest on her waist.

When they parted this time, her gaze was inquisitive. “Have you ever been with a girl before?”

Judging by the way he was shaking, she knew what the answer was, but wanted to hear him say it. “I—no, not—all the way—”

“Do you want to?” she asked, raising a mischievous eyebrow, and he nodded once, mute. He grabbed one of her hands and led her out of the living room, marching down the hallway and into his bedroom. It was plain and unadorned except for a painting of an old sailing ship hanging above his twin bed, with an orange Mets pennant tacked up just behind his door, and two things taped above his desk: a calendar from some kind of bird-watching or nature society, and the pencil sketch that Joan had given him for Christmas.

“It's nice,” she told him, with a little smile.

“Er—do you want me to—what should I—?” He was suddenly shy, and she squeezed his hand in an attempt at reassurance.

“We can just play around first.”

He made an appreciative sound, guiding her to his bed, and they sat there and kissed for a long time. When she slipped her tongue into his mouth, he made a noise like a whimper, clutching at her back with a new desperation, and Joan knew this was the best way to unlock him. She got him onto his back, plucked away his glasses and put them safely on his bedside table, and then she rubbed the palm of her hand against the front of his pants. This earned her a full-body shiver, and another high-pitched noise in the back of his throat.

As she unfastened his trousers, and helped him drag his pants and underwear past his hips, he was breathing hard, staring at her, blue eyes dark and round, and one of his hands teasing over her breasts.

“I—Joan—” he gasped when she teased him in return, straddling his thighs and pumping him with a sure, slow hand. “Christ—I might—”

“It's okay,” she said, moving her hand a little faster, leaning over him a little, and he grabbed her hips with his hands as she touched him for a few minutes, his fingers digging into her sides when he came. It had been quick, but she had expected that, and continued to tease him for several more minutes, until he was half-hard again. Joan loved this part.

“Let me touch you,” he whispered, like it was killing him not to please her in kind, so she unbuttoned her blouse and shrugged out of her brassiere, dropping it on the floor with a raise of her eyebrows and a triumphant noise. Once that happened, he seemed to lose whatever remaining shyness he'd had left. He pulled off his messy t-shirt and rolled them over, pinning Joan to the bed—she laughed in delight, she couldn't help it—and kissed her until she was breathless—kissed her all over, from her mouth to her earlobe to her breasts.

He lingered there. He used his hands and his mouth and asked her what felt good and watched her respond to everything he did until they'd found something that worked, until she was so wound up she wanted to scream. She hadn't been with a boy since just before Christmas—a kid from the junior drama class, whose name she hadn't bothered to learn before going backstage after the musical revue.

“Use your hands,” she whispered, because she needed him, “oh, god, there, just like that.”

He was unsure of himself at first, but could take direction, and with every gasp she made he seemed to gain more confidence—until a few minutes later he had her poised and quivering on the edge of something incredible—oh my god, she was going to—

She arched up into his touch, eyes squeezed closed, hands clutching the sheets, and he guided her through it, then past the breaking point, just like she'd done to him before. She could murder him. She wanted to unravel him.

When she flipped them over, climbed on top of him, and began to move her hips forward, loving the way he felt underneath her, Lane made a noise like a sob.

“You're—oh—you feel—please keep going—”

Joan felt a perverse thrill run through her stomach at the way he babbled, but stopped moving, noticing the way his hips squirmed up at the loss. “If you need help drawing things out, it helps to think unsexy thoughts.”

His voice was ragged. “I—what?”

She shrugged, trying to think of something very practical, then brightened as an idea came to her. “Want me to talk to you about polynomial equations?”

Lane made a choked noise, turning very red. Joan felt him twitch inside her, which almost made her laugh until she saw the deer-in-headlights look in his eyes.

“Oh,” she said gently, bracing her palms on his chest, and gave him a brilliant smile. “Well, in every polynomial equation, there are always two coefficients.”

“You're—wicked,” he gasped in reply, but she was moving her hips again as she spoke, and he was lost, and soon neither of them were talking.

Later, they were lying side by side in his twin bed, Joan with her cheek pillowed on his chest, their clothes scattered all over the floor. Lane took a catnap, but she stayed awake, watching the sunlight from his open blinds play across the room in various shadows. After he woke up, they began to talk a little, about everything and nothing.

“My aunt got a letter the other day,” he said, hesitant. “The Allies are in Germany, and when it's over, I think—Mother will want me to come back to England, but I don't know if—I want to.”

“Kate thinks I'll get into NYU,” Joan murmured in response, not sure what else to tell him that wouldn't sound like an accusation _(go; stay; i know you miss your mom so much_ ) and she traced her fingertips across the planes of his chest, but before she could say anything else, there was the sound of a car pulling into the driveway, and he sat up like he'd been shot out from a cannon.

“Oh, good god, my aunt!”

She had never seen him move so fast, and almost cried laughing at the way he panicked, even as she pulled on her own clothes with haste. When a sharp-faced old woman with iron-gray hair peeked into the room a few minutes later, wearing a suspicious expression and calling her nephew's name, Lane was dressed and sprawled on his stomach across his perfectly-made bed, trying to rescue his pillow from where it was wedged between the foot of the bed and the wall. Joan was also dressed, and perched on the edge of his mirrored dresser, still laughing, gripping his calculus notes in one hand and holding her stomach with the other.

“We were studying polynomial equations,” she managed to gasp out, watching as his argyle-socked feet kicked and flailed in the air. “Oh, my god, are you actually stuck?”

“No,” came the sullen, loud reply, “just—can you please just go out into the hall?!”

“Well, I think you ought to study in the living room,” proclaimed his aunt to no one in particular. Joan couldn't stop laughing long enough to argue about this.

**

At graduation, just after the ceremony ended, she snuck away from the crowded football field for a few minutes, and found Lane standing in their spot, just at the top corner of the gleaming bleachers. Last week, he'd decided to go back to England for school. After that, he didn't know what he wanted to do. She had told him he should do what he thought was right—and then she had cried, and then he had cried—and they hadn't talked much about leaving, after that. It was too painful.

Joan waved to him when he saw her, feeling grown-up in her white graduation robes and new high heels, and when she finally reached him, they hugged for a long time; it must have been several minutes. Her stiff cap was blown off by the wind and got scuffed on the concrete steps, but she didn't notice until Lane picked it up from the ground, turning it over in his hands.

“You didn't write your name in it,” he said softly.

She shrugged, trying to make a joke. “Well, if you've got a pen, you can do it.”

He always had one. She watched him as he took the hat, balanced it over one arm, and printed the letters in careful handwriting. And then he'd kissed her—except in the end, it wasn't her name he had written. She didn't actually look at the inscription until they were driving home in Kate's father's Cadillac, Joan squished between her mother and her best friend in the long leather seat.

Her fingers curled against the vague impression of the letters. Her eyes read it over and over until they blurred with unshed tears. _4x_ _2_ _\+ 6x = f(x)._ It was the factor of a quadratic polynomial. Quadratics always had two identical roots, either real or complex.

Under that were three additional words, his cursive more hurried here. _Always yours. Lane._

“Hey,” whispered Kate, peering over her friend's shoulder at the message scrawled across white cardboard, her expression going soft around the eyes as she put a hand on Joan's arm.

“I'm just happy,” Joan managed to tell the car in a wavering voice, trying to put on a bright face. This time next year, she would be in New York. She'd thought about majoring in math. Everything was going to be new and fun and exciting.

“God. I would never want to be eighteen again,” her mother grumbled aloud, eyeing Joan's tears with an incredulous look, but handing her daughter a tissue all the same.

“You know, you kids don't even realize how lucky you are,” Kate's father said, tapping the brake as they stopped at a red light. “High school's supposed to be the best four years of your lives.”

 

 

 

_epilogue_

Someone rapped loudly on the half-open door. “Good morning, Joan.”

She looked up from her paperwork to see Dawn Chambers standing in front of her desk, and took off her glasses, letting them dangle around her neck. “Morning. Are the quarterly reports printed yet?”

“No,” Dawn said, pulling a face. “Sorry. Donna broke the machine before we could xerox them for the partners' meeting. But you got a letter earlier. Genie couldn't make head or tails of it.”

Joan frowned. “What do you mean?”

The young girl stepped forward, proffering a plain cream envelope and pressing it into Joan's outstretched hand. “You should open it.”

There's nothing remarkable about the envelope—it's postmarked correctly, and from some New York address she doesn't recognize. Joan flipped it around in her hands—the top had already been cut open—and took out the first sheet of paper. Written across the center in dark ink was a line of numbers she hadn't thought about in years:

 _4x_ _2_ _\+ 6x = f(x)_

Followed by two words. _Still yours. Always._

Jesus Christ.

Dawn pretended not to notice that Joan's cheeks had gotten very pink, standing tall and professional, as if the financial chief wasn't blushing like an eighteen-year-old idiot. “Joan?”

“When did this arrive?” Joan blurted, before the young woman could go anywhere. Her voice cracked on the last word, and she winced. “Today?”

“Yes. It—seemed special,” Dawn replied, with a careful shrug. “I thought you'd want to see it for yourself.”

Joan's still staring at the familiar scrawl of handwriting—practically unchanged, and yet so different written out like this, on paper so new it's still stiff around the edges. It can't be him. But it's—god, she does remember so much about that year, those few months they spent together. She still has that scuffed white graduation cap, coated in dust and lying on top of one of her bookshelves. She never had the heart to throw it away. And she's always wondered about Lane in the years since college, when they lost touch—if he stayed in England, if he came back to the States.

“Yes.” She had to clear her throat. Her heart beat quick and furious inside her chest. “Take an early lunch, if you want. I'll tell the girls you had to run a few errands in town.”

“Well, if everything's okay, I'll...leave you alone, then,” said Dawn, giving Joan a tentative smile, and moving to close the door behind her as she left.

Joan sat motionless at her desk for several minutes, then, so quickly it was as if she was trying not to think about the movements, she opened her desk drawer, and took out a brand new sheet of stationery. She sat like this for a few more seconds, her heavy fountain pen poised at the top of the page until she felt she had the courage to form the letters.

The ballpoint nib slid gently against the creamy paper as she wrote.

_Dear Lane—_

 

**Author's Note:**

> Okay, so last week I read [an adorable article](http://www.bostonglobe.com/lifestyle/style/2014/08/22/more-than-years-after-one-summer-together-profession-undying-love/i7q2GErPgqziGScYHNspVJ/story.html?event=event25) about a couple in their 80s and 90s who recently got married after reconnecting, more than 60 years after first falling in love. They met as teenagers working in a biology lab one summer, and wrote notes to each other in mathematical code. So I knew that was going to be put in a fic someday. And then I got this Lane/Joan prompt.
> 
> It's sentimental as hell. It's sheer fluff. TEENS ARE SENTIMENTAL, SO I REGRET NOTHING. Apparently I have a lot of feelings about high school AU fic, because this happened in about a day. And although I have never taken calculus (what's up, algebra three). I hope I did it justice. BRB, I'm going to go cry angsty tears and listen to Vitamin C on repeat. :P
> 
> Also also: I have always pictured young Joan as looking very much like [Holliday Granger in Bonnie & Clyde.](http://www.lifetimetv.co.uk/sites/default/files/styles/max845/public/assets/landscape/Bonnie%26Clyde_Holliday_3470_RT.jpg?itok=-nyKB_KR) Perfect, y/y?


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